The word problem for semigroup presentations having just one defining relation is a major outstanding algebraic decision problem. Semigroup derivation diagrams are analogous to van Kampen diagrams for groups and are a useful graph theoretic tool for studying word problems in semigroups. A feather is a semigroup derivation diagram with the labels removed from the edges. We introduce definitions for the thickness of a feather and we show, that in some situations, a bound upon the thickness of certain feathers would lead to a solution of the word problem over a semigroup presentation.